The solution region for
the previous
example is called
a "closed" or "bounded" solution, because there are
lines on all sides. That is, the solution region is a bounded geometric
figure (a triangle, in that case). You can also obtain solutions that
are "open" or "unbounded"; that is, you will have
some exercises which have solutions that go off forever in some direction.
Here's an example:

Solve the following
system:

2x
– y > –34x
+ y < 5

As usual, I first want
to solve these inequalities for "y".
I get the rearranged system:

y
< 2x + 3y
< –4x + 5

Graphing the
first inequality, I get:

Drawing the second
inequality, I get:

The solution
is the lower region, where the two individual solutions overlap.

The kind of solution displayed
in the above example is called "unbounded", because it continues
forever in at least one direction (in this case, forever downward).

Of course, there's always
the possibility of getting no solution at all. For instance:

But there is no place
where the individual solutions overlap. (Note that the lines y
= x + 2 and
y
= x – 2 never
intersect, being parallel lines with different y-intercepts.)
Since there is no intersection, there is no
solution.